Question

A billfold holds one-dollar, five-dollar, and ten-dollar bills and has a value of $210. There are 50 bills total where the number of one-dollar bills is one less than twice the number of five-dollar bills. How many of each bill are there? Write your answer as an ordered triple in the form (# of one dollar bills, # of five dollar bills, # of ten dollar bills).

Answer 1

There are 29 one-dollar bills, 4 five-dollar bills, and 17 ten-dollar bills.

Step-by-step explanation:

Let's assign variables to represent the number of each type of bill. Let's say x represents the number of one-dollar bills, y represents the number of five-dollar bills, and z represents the number of ten-dollar bills.

According to the information given, we can set up the following equations:

1. x + y + z = 50 (because there are 50 bills total)
2. x = 2y - 1 (because the number of one-dollar bills is one less than twice the number of five-dollar bills)
3. 1x + 5y + 10z = 210 (because the total value of the bills is $210)

We can solve this system of equations to find the values of x, y, and z.

Substituting the value of x in the second equation, we get 2y - 1 + y + z = 50, which simplifies to 3y + z = 51.

Rearranging the first equation, we get z = 50 - x - y. Substituting these values into the third equation, we get 1x + 5y + 10(50 - x - y) = 210.

Simplifying this equation, we get -4x - 4y = -290. Solving these two equations simultaneously, we find that x = 29, y = 4, and z = 17.

Therefore, there are 29 one-dollar bills, 4 five-dollar bills, and 17 ten-dollar bills.